I assume familiarity with vector and topological spaces, and with the standard model of the real numbers. I assume that you know the basic facts about metric spaces, normed and seminormerd spaces, Banach and Hilbert spaces.
On successful completion of this course, the student should:
- Know the fundamental fixed point theorems for set-valued maps and the basic existence results for equilibrium problems and variational inequalities.
- Explain some interconnections among these various results.
- Apply this analysis to game and economic theory
The Knaster-Kuratowski-Mazurkiewicz lemma
Brouwer's fixed point theorem
Variational inequalities and equilibrium problems
Generalized monotonicity and convexity
Brézis-Nirenberg-Stampacchia theorem and Fan's minimax principle
Continuity of correspondences
Browder, Kakutani and Fan-Glicksberg fixed point theorems
Nash equilibrium of games and abstract economies
Walrasian equilibrium of an economy
An application to traffic network